By Werkle H.
Die Methode der Finiten Elemente ist heute ein Standardverfahren zur Berechnung von Flächentragwerken im konstruktiven Ingenieurbau mit Hilfe des pcs. In diesem Buch werden die theoretischen Grundlagen der Methode für Stab-, Platten- und Scheibentragwerke dargestellt, soweit sie für das Verständnis des Verfahrens und eine qualifizierte Anwendung erforderlich sind. Hierbei werden auch die wichtigsten, in kommerzielle Finite-Element-Software implementierten Elementtypen und deren Eigenschaften untersucht. Darüber hinaus werden Fragen der Modellbildung ausführlich behandelt und Hinweise zur Interpretation der Ergebnisse gegeben. Anhand einer Reihe von Beispielen werden wesentliche Aussagen verdeutlicht. Das Buch richtet sich an praktisch tätige Ingenieure sowie an Studierende der Fachhochschulen und - soweit die Anwendung der Finite-Elemente-Methode im Vordergrund steht - auch der Technischen Hochschulen. Es hat zum Ziel, zu einem vertieften Verständnis der Finite-Elemente-Methode und der qualifizierten Interpretation der mit ihr erhaltenen Ergebnisse in der Praxis beizutragen.
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Extra info for Finite Elemente in der Baustatik. Band 1: Lineare Statik der Stab- und Flächentragwerke
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1 in connection with the Kelvin principle leads to a symmetric, weakly coercive mixed-Galerkin formulation for the equations of linear elasticity. 4 Examples 27 and the minimization problem min v∈[H01 (Ω )]d JS (v; f) ∇ · v = 0 in Ω . 58) is a constrained optimization problem. Lagrange multiplier method. 58) by introducing a Lagrange multiplier p ∈ L02 (Ω ) and the Lagrangian functional LS (v, p; f) = JS (v; f) − p∇ · v dΩ . 58) is transformed into the unconstrained optimization problem of finding the saddle points {v, p} ∈ [H01 (Ω )]d × L02 (Ω ) of LS (v, p; f).
34) but make the resulting algebraic systems easier to solve are referred to as enhanced methods. 9) as an abstract setting for a brief overview of the many modifications that have been proposed. 9). 9) seek to make the discrete systems “easier” to solve. In come cases, they also result in a reduction of the Tikhonov regularization for which the original problem is perturbed into a problem that is wellposed and/or easier to solve. , [337]), a process that involves the construction of an externally defined problem.
15) that allow for the elimination of ph and for the replacement of the indefinite saddle-point matrix by a positive definite matrix. 10). 15). 34). 10) is defined by a single discrete space, it seems reasonable to assume that that problem is well-posed as long as V h ⊂ V . Unfortunately, this is not true. 10) can be converted to T Ah Bh vh Bh −εIh ph = dh 0 . 10) remains associated with a saddle-point formulation in which the space Sh is implicitly defined from V h by Sh = BhV h ; see [273]. 10) is contingent upon the compatibility of V h and the implicitly defined space Sh .